Question

Need help with a problem. For some reason I can not seem to get it correct. Thinking my formula is wrong. Here's the problem:

Assume that there are approximately 140x10^9 stars in our galaxy.
Our galaxy is 50,000 light years from the center to the edge, but just 1,000 light years thick. It's shaped like a thin disk or cylinder. If the stars were distributed equally throughout the galaxy, how many stars would you expect to find in one cubic light year?

I thought it would be Pi*r^2*l. Then divide that by the number of stars. What am I doing wrong? Thanks, been 20 years since I had to do math like this!

Answer 1

$r=50,000\text{ ly}=5\cdot10^4\text{ ly}\\ h=1,000 \text{ ly}=10^{3}\text{ ly}\\ V=\pi r^2h\\\\ V=\pi \cdot(5\cdot10^4)^2\cdot10^3\\ V=\pi \cdot25 \cdot10^8 \cdot10^3\\ V=2.5\pi\cdot10^{12} \text{ ly}^3\\\\ \dfrac{140\cdot10^9}{2.5\pi\cdot10^{12}}=\\ \dfrac{1.4\cdot10^{11}}{2.5\pi\cdot10^{12}}=\\ 0.56\pi\cdot10^{-1}=\\ 5.6\pi\cdot10^{-2}\approx1.76\cdot10^{-1}$